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forum.virtualchallengemeets.com • View topic - Transcendental #s

Transcendental #s

What could be so hard. It's a multiple-choice test for Pete's sake.

Transcendental #s

Postby collegebookworm » Sat Apr 07, 2007 12:36 pm

On District 2, #19:

19. Which of the following is NOT a transcendental number?

(A) 1.6180339887... (B) 2.7182818285... (C) .3245324532...
(D) 3.1415926536... (E) 0.6180339887...

The correct answer is (C), since that value is the solution to 9999x - 3245 = 0.
Aren't the golden ratio [unparseable or potentially dangerous latex formula] (A) and its inverse [unparseable or potentially dangerous latex formula] (E) both NOT transcendental as well?

My equations were:
([unparseable or potentially dangerous latex formula]) [unparseable or potentially dangerous latex formula] for the positive square root, and
([unparseable or potentially dangerous latex formula]) [unparseable or potentially dangerous latex formula] for the positive square root
(NS/CA/MA/CS/SC) "**" indicates TMSCA State
08 HI(LO): 142?-**(88-D2)/224-D2(17x-**)/320-D2(202-**)/248?-D2(206-**)/210-D2(17x-NovA+?)
08 D2: 88/224/320/210/248

Next meet: Texas Tech (Region, 4/11-12)
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Postby AuSmith » Sat Apr 07, 2007 1:08 pm

Uh huh...
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Postby Kurt » Sat Apr 07, 2007 1:32 pm

Yeah, all three are algebraic. When I took this test in practice, I chose the continued fraction since it seemed to be obviously what he wanted.

He might have been using this definition:
[unparseable or potentially dangerous latex formula] to validate [unparseable or potentially dangerous latex formula] as transcendental...although if a number is a root to any polynomial equation with integer coefficients, it is supposed to be algebraic..so I don't think he thought it all the way through. (That definition above can easily be rewritten as the polynomial equation by expanding the hyperbolic sine function using its definition.)
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Postby ZachB » Sat Apr 07, 2007 4:36 pm

The golen ration is an algebraic irrational number, but not transcendental.
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Postby AuSmith » Sat Apr 07, 2007 4:59 pm

It's likely that he just wanted to change from irrational to transcendental and didn't get to change the choices... (why we need editors?)
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